A selective reduction-type NOx catalyst (hereinafter, simply referred to as a “NOx catalyst”) is known which purifies NOx contained in exhaust gas from an internal combustion engine using ammonia as a reducing agent. An adding valve or the like that adds ammonia or an ammonia precursor into exhaust gas is installed on an upstream side of the NOx catalyst. An ammonia precursor can be exemplified by urea. Hereinafter, an ammonia precursor or ammonia will also be collectively referred to as a “reducing agent”.
In this case, in order to maintain a NOx purification rate of the NOx catalyst at a high level, a certain amount of reducing agent must be adsorbed by the NOx catalyst in advance. Therefore, supply of the reducing agent may be performed from the adding valve or the like based on a difference between an amount of the reducing agent to be adsorbed by the NOx catalyst (hereinafter, also referred to as a target adsorption amount) and an amount of the reducing agent estimated to be adsorbed by the NOx catalyst (hereinafter, also referred to as an estimated adsorption amount) (for example, refer to Patent Document 1). Moreover, a NOx purification rate is an amount of NOx purified by a NOx catalyst with respect to an amount of NOx that flows into the NOx catalyst. Alternatively, a NOx purification rate may be considered a NOx concentration in exhaust gas that is reduced due to purification by a NOx catalyst with respect to a NOx concentration in exhaust gas that flows into the NOx catalyst.